Abstract

This paper presents a new class of chaotic systems with infinite number of equilibrium points like a 3-‎leaved clover. They signify an exciting class of dynamical systems which represent many major ‎characteristics of regular and chaotic motions. These chaotic systems belong to the general class of ‎chaotic systems with hidden attractors. By using a systematic computer search, three chaotic systems ‎with 3-leaved-clover-shaped equilibria were found which are classified to dissipative systems. ‎Dynamics of the chaotic system with the 3-leaved-clover-equilibria has been investigated by using ‎phase portraits, bifurcation diagram, Lyapunov exponents, Kaplan-Yorke dimension and Poincaré map. ‎Moreover, an electronic circuit implementation of the theoretical system is designed to check its ‎effectiveness. RNG (random number generator) design has been realized with new developed chaotic ‎systems. The obtained random bit sequences are used for image encryption. Security analysis of image ‎encryption processes has been performed.‎